HEREDITY 



299 



of each series is derived from the series itself. There 

 is more than one kind of them, but they are all 

 mutually convertible, just as measures recorded in 

 feet are convertible into inches. The most con- 

 venient unit for purpose of explanation, though not 

 for calculation, is the half difference between the 

 marks or measures corresponding to the lower or 

 to the upper quartiles respectively. 1 



Deviations expressed in statistical units are 

 usually found to conform with much closeness to 

 the results of a certain theoretical law, discovered 

 by Gauss, the great mathematician, and properly 

 called by his name, though more familiarly known 

 as the Normal Law. It supposes all variability to be 

 due to different and equally probable combinations 

 of a multitude of small independent causes. The 

 relative frequency of different amounts of these, 

 reckoned in statistical units, can thence be computed. 

 It is done by refined methods based on the same general 

 principles as those by which sequences of different 

 lengths, in successive throws of dice, are determined. 



Results of the computation are shown in the bottom 

 line of the following small table : 



Gentiles and Corresponding Deviation from the Median. 



1 This unit is known by the uncouth and not easily justified name of 

 " Probable Error," which I suppose is intended to express the fact 

 that the number of deviations or "Errors" in the two outer fourths 

 of the series is the same as those in the two middle fourths ; and 

 therefore the probability is equal that an unknown error will fall into 

 either of these two great halves, the outer or the inner. 



